Serpentine fluid reactor components

ABSTRACT

Some embodiments of the present invention provide components for a serpentine fluid reactor which is optimized for one or more objective functions of interest such as pressure drop, erosion rate, fouling, coke deposition and operating costs. The components are designed by computer modeling the components individually and collectively in which the cross section of flow path is substantially circular under industrial conditions to validate the model design and its operation. Then iteratively the component designs are deformed and the operation of the deformed part(s) is modeled and compared to values obtained with other deformed models until the value of the objective function is optimized (e.g. at an extreme) or the change in the objective function is approaching zero.

FIELD OF THE INVENTION

Some embodiments of the present invention relate to components for andan integrated fluid serpentine reactor. The fluid could be a liquid andthe reactor could be for example a high pressure polyethylene reactor.The fluid could be a gas and serpentine reactor could be a cracker forhydrocarbons such as ethane to ethylene.

In one aspect the present invention relates to the individual components(e.g., pipes, “U” bends, “90 degree bends” and “wyes”) and the assembledcomponents for furnaces for cracking paraffins to olefins, particularlyfor the production of ethylene. In the cracking of paraffins to produceolefins, and particularly alpha olefins, a feed stock, for example, alower paraffin such as ethane or naphtha, is heated to a temperature ofat least about 850° C., or from about 900° C. to 1000° C. In the processthe molecules in the feed stock loose hydrogen and become olefins. Thisprocess takes place in the heater coils inside the furnace in theradiant box of the ethylene cracker. The hot gases leaving the furnaceare quickly fed to a quench exchanger.

BACKGROUND OF THE INVENTION

To date the components for a cracker or a high pressure ethylene reactorhave been circular in cross-section. The consideration of the cost ofmanufacture relative to efficiency of the reactor in terms of pressuredrop and erosion rate has been largely weighted to minimize the cost ofmanufacturing. Hence the components have circular cross sections. Withthe increase in the price of feedstocks both for the cracking processand the furnace and the concern about green house gas emissions theweighting of the factors in the design of components is starting to movetoward the efficiency of the process. Several factors to be consideredin the efficiency of the furnace include the pressure drop across (i.e.,along the length of) the cracker the erosion rate of the components ofthe reactor and the degree of recirculation of the flow which relates tofouling (e.g., coke deposition).

Methods for designing a material handling system using computer selectedparts from a catalogue or inventory of parts are directed at assemblingpre-existing parts are known, but do not disclose or teach the designingof new parts.

There are methods to use computer assisted design (CAD) to initiallygenerate drawings for a pipe network based on a standard pipe sizes.That system does not disclose the design of “custom” pipe or a customelbow, etc., to use either alone or in combination with standard pipesizes.

There are computer programs to estimate “wall thinning”. The process isbased on measurements of pipe erosion and modeling the fluid flowthroughout the entire pipe network or system to predict the rate of wallthinning at a point distant from the actual measurement. This is thenused to predict the locations of potential pipe failure and to schedulemaintenance of the pipe network to minimize “down time”. The designingof individual components for the pipe network to minimize pressure dropand erosion is not disclosed.

As far as applicants have been able to determine there is no artsuggesting a non-circular cross section for the components (e.g., pipes,bends and wyes individually or in combination) for a serpentine fluidreactor such as an olefins (ethylene or propylene) cracker or a highpressures ethylene polymerization reactor.

A need exists for components individually and collectively for a fluidserpentine reactor which is fabricated to minimize any one of orcombinations of pressure drop, fouling, recirculation, erosion in thecomponent(s), the assembled reactor, or both and cost (operating,capital or both).

SUMMARY OF THE INVENTION

In one embodiment, the present invention provides one or more componentsfor a fluid serpentine reactor said one or more components having aninternal flow passage having a continuously smooth and differentiableperimeter and centerline and a smoothly varying cross-section along theflow passage such that in the about 5% of the flow passage from theinlet and the outlet the ARQ is from about 1.0 to about 1.02 and overthe remain about ing 90% of the length of the flow passage not less thanabout 5% of the flow passage has an ARQ is from about 1.02 to about 1.5.

In a further embodiment, the fluid serpentine reactor is a high pressureolefin polymerization reactor.

In a further embodiment, the fluid serpentine reactor is an olefin, forexample, ethylene or propylene, cracker.

In a further embodiment, the ARQ over said remaining about 90% of thelength of the flow passage for said component does not change by morethan about 7% over an about 5% length of the flow path.

In a further embodiment, the ARQ at one or more sections over saidremaining about 90% of the length of the flow passage for said componentis from about 1.02 and about 1.30.

In a further embodiment the ARQ over said remaining about 80% of thelength of the flow passage for said component does not change by morethan about 5% over an about 5% length of the flow path.

In a further embodiment, the calculated total pressure drop across thecomponent, or reactor, is decreased by not less than about 10% comparedto the calculated pressure drop for the component, or reactor, having anARQ along its length from about 1.00 to about 1.02.

In a further embodiment, the ARQ at one or more sections over saidremaining about 80% of the length of the flow passage for said componentis from about 1.02 and about 1.15.

In a further embodiment, the normalized calculated erosion rate of thecomponent is decreased by not less than about 10% compared to thenormalized erosion rate for the component having an ARQ along its lengthfrom about 1.00 to about 1.02.

In a further embodiment, the component has, a smooth curve in itslongitudinal direction which although may change rapidly, does notinclude abrupt, sharp changes of internal section (steps) has a radiusof curvature on the internal surface of the curve from unbound(straight) to half the vertical of the section radius.

In a further embodiment, the component comprises from about 20 to about50 weight % of chromium, about 25 to about 50 weight % of Ni, from about1.0 to about 2.5 weight % of Mn less than about 1.0 weight % of niobium,less than about 1.5 weight % of silicon, less than about 3 weight % oftitanium and all other trace metals and carbon in an amount less thanabout 0.75 weight % and from about 0 to about 6 weight % of aluminum.

In one embodiment, the present invention provides a method to optimizeone or more of the operating characteristics selected from pressuredrop, erosion rate, fouling rate, and cost (capital, operating or both)of a fixed industrial flow path defined by a continuous metal and/orceramic envelope, comprising:

-   -   building a computational model comprising not less than about        5,000, or more than about 100,000, computational cells for all        or a portion of the flow channel from about 5% of the length of        the flow channel downstream of the inlet to from about 5% of the        length of the flow channel upstream of the outlet of the initial        design of said industrial flow path;

using computer software that solves the fundamental laws of fluid andenergy dynamics for each cell simulating and summing the results theoperation of the model design from step 1 under the industrial pressure,temperature, and flow rate conditions of operation to verify one or moreobjective functions of interest (e.g. pressure drop, erosion rate,fouling, coke deposition and cost) to match operating conditions;

iteratively;

deforming said computational model comprising not less about 5,000computational cells so that the resulting ARQ of one or more sections ofthe flow path is greater than about 1.02;

applying the same computer software as in step 2, that solves thefundamental laws of fluid and energy dynamics for each cell simulatingand summing the results of the operation of the deformed model from step3 a) under the industrial pressure, temperature, and flow rateconditions of operation used in step 2 to predict one or more objectivefunctions of interest (e.g., pressure drop, erosion rate, fouling, cokedeposition and cost) for the operation of the deformed model;

storing the predicted results from step 3 b);

using some or all of the stored results from step 3 c) with anoptimization algorithm to estimate a deformation that will improve theobjective function;

repeating steps a), b), c), and d) until one or both of the followingconditions are met:

the objective function of interest goes through a beneficial localextrema; or

-   -   ii) the rate of change of all of the all the functions of        interest starts to approach 0.

wherein the computational model has from about 10,000 to about 100,000computational cells, in one embodiment.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, benefits and aspects of the present invention are bestunderstood in the context of the attached figures in which like parts orfeatures are designated by like numbers.

FIG. 1 shows different cross sections of a flow path having an ARQgreater than 1.

FIG. 2 shows a series of overlays of equal perimeter ellipses havingdifferent ARQ equal to or greater than 1.

FIG. 3 is an isometric view of a serpentine reactor for the cracking ofparaffins to olefins as an example of prior art.

FIG. 4 shows multiple views of a U bend or an about 180 degree bend inaccordance with the present invention.

FIG. 5 is a sectional view along the flow path of FIG. 4 and crosssections at A, B, C, D and E.

DETAILED DESCRIPTION

Other than in the operating examples or where otherwise indicated, allnumbers or expressions referring to quantities of ingredients, reactionconditions, etc. used in the specification and claims are to beunderstood as modified in all instances by the term “about.”Accordingly, unless indicated to the contrary, the numerical parametersset forth in the following specification and attached claims areapproximations that can vary depending upon the desired properties,which the present invention desires to obtain. At the very least, andnot as an attempt to limit the application of the doctrine ofequivalents to the scope of the claims, each numerical parameter shouldat least be construed in light of the number of reported significantdigits and by applying ordinary rounding techniques.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the invention are approximations, the numericalvalues set forth in the specific examples are reported as precisely aspossible. Any numerical values, however, inherently contain certainerrors necessarily resulting from the standard deviation found in theirrespective testing measurements.

Also, it should be understood that any numerical range recited herein isintended to include all sub-ranges subsumed therein. For example, arange of “1 to 10” is intended to include all sub-ranges between andincluding the recited minimum value of 1 and the recited maximum valueof 10; that is, having a minimum value equal to or greater than 1 and amaximum value of equal to or less than 10. Because the disclosednumerical ranges are continuous, they include every value between theminimum and maximum values. Unless expressly indicated otherwise, thevarious numerical ranges specified in this application areapproximations.

All compositional ranges expressed herein are limited in total to and donot exceed 100 percent (volume percent or weight percent) in practice.Where multiple components can be present in a composition, the sum ofthe maximum amounts of each component can exceed 100 percent, with theunderstanding that, and as those skilled in the art readily understand,that the amounts of the components actually used will conform to themaximum of 100 percent.

The present invention will further be described by reference to thefollowing examples. The following examples are merely illustrative ofthe invention and are not intended to be limiting. Unless otherwiseindicated, all percentages are by weight unless otherwise specified.

As used in this specification relatively smoothly in relation to the ARQmeans the quotient does not change by more than about 7% over an about5% length of the flow path.

As used in this specification smooth in relation to the perimeter of theflow passage means the perimeter at an angle perpendicular to the flowis a differentiable continuous smooth line (i.e., having no kinks ordiscontinuities). As a result the perimeter of the flow passage will notbe a geometric shape having straight sides and “corners” or “angles”such as a square, a parallelogram or a triangle. Rather the perimeter ofthe flow passage is defined by a continuous smooth curved line.

As used in this specification smooth in relation to the center line ofthe flow passage means the center line of the flow passage is adifferentiable continuous smooth line (i.e., having no kinks ordiscontinuities, or having substantially no kinks or substantially nodiscontinuities). While the center line of the flow passage may changerapidly, it will not include abrupt, sharp changes of internal section(steps).

As used in this specification building a computational model meanscreating a virtual three dimensional geometric model of one or morecomponent(s) or a reactor and filling it with a three dimensionalcomputational mesh to create cells (e.g. about 5,000, or about 50,000,or about 100,000 cells, or optionally greater than about 100,000 cells).

ARQ is defined as the ratio of aspect ratio (AR) to isoperimetricquotient (Q) of a section or segment of the flow passage perpendicularto the direction of flow (AR/Q). The aspect ratio (AR) is defined as theratio of long to short side of the smallest-area rectangle into which aparticular section can be circumscribed. This ratio, for the case of aconvex ovoid section symmetric about one axis, is equal to the ratio ofthe major chord to minor chord. The major chord is the length of thelongest straight line between two points in the perimeter of a closedsection which may or may not cross the centroid of the section. Theminor chord for such a section is the longest distance perpendicular tothe major chord between two points along the perimeter of the section.It will appear clear to those skilled in the art that thus defined theaspect ratio is greater than one.

AR=Long/Short

The isoperimetric quotient is defined as four times Pi (π) times theArea of the section of the flow path divided by the square of thatsection's perimeter. At a cross section of the flow path if the area ofthe cross section is A and the perimeter is L, then the isoperimetricquotient Q, is defined by

$Q = \frac{4\pi \; A}{L^{2}}$

The isoperimetric quotient is a measure of circularity. This isillustrated in FIG. 1 and FIG. 2.

A circle has a cross-sectional shape with an isoperimetric quotient ofone and all other cross-sectional shapes have an isoperimetric quotientless than one.

Since the ARQ ratio is the aspect ratio (AR) divided by theisoperimetric quotient (Q) and as defined AR is greater than one and Qis less than one, ARQ is also greater than one and greater than or equalto the aspect ratio.

FIGS. 1 and 2 demonstrate that even an ARQ near but not equal to 1 canbe noticeably non-circular.

Sample Calculation of an ARQ Ratio:

An ellipse with a major radius “a” and a minor radius “b” has a crosssectional area A=Pi*a*b. The perimeter of such an ellipse can beapproximated by Ramanujan's formula which states the perimeter of anellipse being approximately:

L≈π[3(a+b)−√{square root over ((3a+b)(3b+a))}]

For a particular example of an ellipse having a major radius “a” equalsfour times the minor radius “b”, it would have an Area A=4*π*b². Thisfour-to-one ellipse has a perimeter L

L≈π[3(5b)−√{square root over ((12b+b)(3b+4a))}]

L≈π[15b−√{square root over (91b ²)}]≈5.461πb

So a four-to-one ellipse has an isoperimetric quotient Q equal

$Q \approx \frac{16\pi^{2}b^{2}}{29.822\pi^{2}b^{2}} \approx 0.537$

And since the aspect ratio of this section is 4, the ARQ of such asection is 7.45.

In comparison, standard pipe has an out-of round tolerance of plus orminus about 1.5% and as such, the maximum ARQ of a nominally roundsection is approximately 1.0151.

FIG. 3 is an isometric drawing of a prior art of a serpentine paraffincracking reactor up to the transfer line exchanger. The serpentinereactor comprises one or more inlets 1, multiple about 90 degree elbows2, multiple U bends or about 180 degree bends 3, a flow combining wye 4and an outlet or exit 5. Flow passage components 2, 3, and 4 areexamples of components whose optimization is the subject of oneembodiment of the present invention.

In FIG. 3 cross sections at all positions along the serpentine reactorlength are circular having an out-of round tolerance of, for example,plus or minus about 1.5% and as such, the maximum ARQ of a nominallyround section is approximately 1.0151.

In the components of the prior art the flow path was circular along itsentire length albeit expanding as described below and the ARQ along theserpentine reactor is substantially 1 (e.g. from about 1.0 to about1.02).

The cross sectional area of the flow path varies smoothly from a minimumto a maximum area along the length of the components in the direction offlow of the gas but all cross-sections are substantially round with anARQ of 1 other than by unintentional variations of tolerance plus orminus about 2% (Maximum ARQ of about 1.02).

FIG. 4 has several views of a component, a “U” bend (in accordance withone embodiment of the present invention comprising).

The U bend 30 an inlet 31 a body 32, and exit or outlet 33. The hot gasfrom the cracker enters at the inlet 31, passes through the body 32turns through about 180 degrees and exits at 33. The inlet 31 and exit33 of the “U” bend is circular or substantially circular. 32 is a sideview, 34 is a bottom view, 35 an isometric view, and 36 is and end viewof the component (“U” bend”).

FIG. 5 shows a sectional view of the component (“U” bend) of FIG. 4 inaccordance with one embodiment of the present invention. The crosssections at A-A, B-B, C-C, D-D and E-E as well as the inlet and outletare also shown. The cross section at the inlet 31 and exit 33 in FIG. 4of the “U” bend are substantially circular. However, the cross sectionsas A-A, B-B, C-C, D-D, and E-E have respective ARQ values of 1.02,1.114, 1.94, 1.12, and 1.02. Clearly, cross sections, B-B, C-C, and D-Dare not circular. Arguably cross sections A-A and E-E are not circular.

In this embodiment the ARQ varies smoothly from 1 at either end (inlet31 and exit 33 (round furnace pipe at both ends)) but reaches a maximumnon-roundness with a maximum ARQ of 1.94 at C-C.

The shape of the cross section of the flow path may be elliptical,ovoid, segmented or asymmetric in nature. The area of the cross-sectionmay also be held constant, increase or decrease according to thefunction to be achieved. A twist may optionally be imposed on adjacentcross sections either by means of interior swirling vanes or beads(e.g., a welded bead on the interior of the pipe) within the serpentinereactor or by the bulk twisting of the cross sections relative to eachother.

However, it should be noted that different shapes may have a comparableARQ and that a low change in the quotient may in fact result in asignificant change in the cross section shape of the flow path such asfrom a near ellipse to a “flattened egg shape.” This is demonstrated inFIGS. 1 and 2. An about 1% change in ARQ can have a profound effect onthe flow characteristics as indicated by pressure drop, for example.

The cross section of the component within the last about 5% of the flowpath from the inlet and exit or outlet of the component have an ARQapproaching unity from above, or from about 1.02 to about 1.0, or fromabout 1.01 to about 1. This helps with component assembly and reducesredundancy of comparable components.

In the remaining about 90% of the flow path there are one or moresections where the ARQ is from about 1.02 to about 1.50, or from about1.02 to about 1.3, or from about 1.02 to about 1.12. The interior of theflow path is “smooth” in the sense that the change in the ARQ in about5% sections of the remaining flow path does not change by more thanabout 7%, or less than about 5%.

The shape of the cross sections of the flow path is optimized to obtaina local beneficial minimum or maximum (known collectively as “extrema”)of an objective function. Such objective function may be any parameteraffecting the economics of the operation of the transfer line includingthe cost (capital and or operating) itself include but is not limited topressure drop, erosion rate of the fluid-contacting surfaces, weight ofthe component, temperature profile, residence time and rate of fouling(or coke deposition).

There are a number of software applications available which are usefulin one embodiment of the present invention. These include SolidWorks forthe creation and parametric manipulation of the flow geometry, ANSYSMechanical for the calculation of material stress and ANSYS Fluent todetermine the flow pattern, pressure drop and erosion rate used incalculating the objective function corresponding to a particulargeometry.

Procedurally, one way to find a local objective function extremum is bysequentially applying a small perturbation to a parameter affecting theshape of the component and determining the resulting value of theobjective function by either analytical techniques, experiments ornumerical computation. A deformation parameter is defined as a valuewhich can be uniquely mapped to a change in geometry by means ofscaling, offsetting or deforming any or all of the sections in adeterministic fashion. Each parameter may also be bounded to preventgeometric singularities, unphysical geometries or to remain within theboundaries of a physical solution space. After each of a finite andarbitrary number of parameters has been perturbed, any one of a seriesof mathematical techniques may be used to find the local extremum. Inone such technique a vector of steepest approach to the objectivefunction extremum is determined as a linear combination of parameterchanges. The geometry is progressively deformed in the direction ofsteepest approach and the value of the objective function determined foreach deformation until a local extremum is found. The process is thenrestarted with a new set of perturbations of the parameter set. Othertechniques that may be used to advance the search for a local extremuminclude Multi-objective genetic algorithms, Metamodeling techniques, theMonte Carlo Simulation method or Artificial Neural Networks.

For example a model of the original design is built. That is a threedimensional finite model of the component is created. The model includesthe internal flow passage (void) within the component. The model mayalso include the external surface of the component. The model may thenbe divided into (or filled with) cells, for example, at least about5000, or from about 5,000 to about 10,000, or from about 10,000 to about100,000, or optionally more than about 100,000 (e.g. about 150,000, orabout 200,000, or about 250,000, or about 500,000) cells. To some extentthis is dependent on computing power available and how long it will taketo run the programs for each deformation of the original model. Thereare a number of computer programs which may be used to build theoriginal model such as for example finite element analysis software(e.g. ANSYS Mechanical).

Then the model needs to be “initialized”. That is a fluid dynamics andenergy (of mass, energy and momentum etc.) dynamics computer program isapplied to each cell of the model to solve the operation of that cell atgiven operating conditions for the component (e.g. mass of gas passingthrough the component, flow velocity, temperature, and pressure, erosionrate, fouling rate, recirculation rate etc.) to calculate one or moreobjective functions. The sum of the results of each cell operationdescribes the overall operation of the component. This is runiteratively until the model and its operation approach, or closely matchactual plant data. The model should be initialized so that for one ormore of objective functions, the simulation is within about 5%, orwithin about 2%, or within about 1.5% of the actual plant operating datafor that objective function of the transfer line exchanger. One fluidand/or energy dynamics program which is suitable for the simulation isANSYS Fluent

Once the design of the component and its operation is initialized themodel of the component is iteratively deformed, for example, in a smallmanner but incremental manner and the simulated operation of thedeformed part is run to determine the one or more objective functionsfor the deformed component (for the cells and the sum of the cells oreven cells in specified location or regions (at the internal radius ofcurvature of a bend). The deformation may be applied to all or part ofthe flow channel of the component within about 5% of the flow channeldownstream of the inlet to about 5% of the flow channel upstream of theexit (i.e. about 90% of the component is available for deformation). Insome instances the deformation may occur in one or more sections orparts within about 10% of the flow channel downstream of the inlet toabout 10% of the flow channel upstream of the exit (i.e. about 80% ofthe component is available for deformation). While the deformation couldbe applied to the whole length of component available for deformation itmay be useful to apply the deformation to sections or portions of thecomponent. For example the last or first half, third or quarter orcombinations thereof could be deformed. The results (e.g. one or moreobjective functions and the sum of each such objective function) of thesimulated operation of the deformed component are stored in thecomputer.

The deformation of the component may be accomplished by applying afurther computer program to the design which incrementally deforms thepart. One such commercially available deformation and optimizationsoftware is sold under the trademark Sculptor. However, tone may use aneural network to optimize the location and degree of deformation tospeed up or focus the iterative process.

The stored calculated objective function(s) for the operation of thedeformed component are then compared until either:

an extrema of one or more objective functions is reached; or

the rate of change in the one or more objective functions is approachingzero.

In some embodiments, the present invention provides a method to optimizeone or more of the operating characteristics of a fixed industrial flowpath defined by a continuous metal envelope, selected from pressuredrop, erosion rate, and coke deposition rate comprising:

building a numerical model comprising not less than about 5,000, oroptionally more than about 100,000, computational cells of the portionof the flow channel for example, from about 5% of the flow channeldownstream of the inlet and to about 5% of the flow channel upstream ofthe outlet (e.g. about 90% of the of the flow channel of the transferline) of the initial design;

simulating (on a computational cell level and summed) the operation ofthe model design from step 1 using fluid and energy dynamics softwareunder the industrial pressure, temperature, and flow rate conditions ofoperation to numerically determine one or more of the functions ofinterest (pressure drop, erosion rate, fouling rate and cost (capitaland operating)) approach (within about 5%) or match actual operatingconditions;

iteratively;

deforming said numerical model comprising not less about 5,000computational cells by deforming the geometry such that the resultingARQ of the section is materially greater than about 1.02;

simulating the operation of the deformed model under the plant operatingconditions used in step 2 to determine one or more objective functionsof interest (e.g. pressure drop, erosion rate, fouling rate, and cost(capital and/or operating);

calculating and storing said one or more of functions of interestcalculated in step b);

using some or all of the stored results from step 3 c) with anoptimization algorithm to estimate a deformation that will improve theobjective function;

comparing the stored objective functions of interest until one or bothof the following conditions are met:

the objective function reaches a desirable local extrema; or

ii) the objective function ceases to change in the parametrizeddirection.

Some objective function value, for example pressure drop and erosionrate, at each evaluation stage in the process of finding the localextremum can be obtained via Computational Fluid Dynamics. If the changein transfer line cross-sections along the flow path is selected so thatthe calculated total pressure drop across the line decreases by about10% from the baseline condition made of standard components (i.e. wherethe ARQ is from about 1 to about 1.02 along the about 90% or about 80%of transfer line flow path) which is used as a comparison benchmark andthe erosion rate of the line is decreased by more than about 5% comparedto the baseline calculated using a combination of structural finiteelement analysis software; computational fluid dynamics simulation ofthe flow rate and a geometry manipulating software that alters the shapeof the transfer line in a parametric fashion.

In some embodiments the models will be run until the change in objectivefunction between successive iterations is less than about 10% or lessthan about 1%. In one embodiment when compared to a baseline of aconventionally designed component, the present invention has a decreasein total pressure drop of over about 10% and the subsequent erosion rateand fouling rate is also affected and decreased when compared to thebaseline conditions. This decrease is at least in the order of magnitudeof the total pressure drop. In an optional embodiment the fouling (e.g.coke deposition) rate of the component is also determined. The foulingrate as noted below is also a function of the metallurgy of thecomponent and the surface coating in the flow channel of the component.

The fouling rate for the component should be less than about 0.1mg/cm²/hr, or less than about 0.07 mg/cm²/hr, or less than about 0.05mg/cm²/hr, or less than about 0.03 mg/cm²/hr, or less than about 0.02mg/cm²/hr. The coke rate may be affected by a number of factorsincluding the cross sectional shape of the component and the metallurgyof the component. In one embodiment for computer simulations themetallurgy of the transfer line may be considered constant and after thepreferred shape is determined the metallurgy of the component of theserpentine reactor may be selected.

The components for the serpentine reactor may be constructed fromstainless steel. In some embodiments the steel has a surface which tendsto mitigate the formation of coke such as that disclosed in U.S. Pat.No. 6,824,883 issued Nov. 30, 2004 to Benum et al. assigned to NOVAChemicals International S.A.

In one embodiment, the steel has a high nickel and chrome content.

In one embodiment the stainless steel comprises from about 20 to about50, or from about 20 to about 38 weight % of chromium and at least about1.0 weight %, up to about 2.5 weight % or not more than about 2 weight %of manganese. The stainless steel should contain less than about 1.0, orless than about 0.9 weight % of niobium and less than about 1.5, or lessthan about 1.4 weight % of silicon. The stainless steel may furthercomprise from about 25 to about 50 weight % of nickel, from about 1.0 toabout 2.5 weight % of manganese and less than about 3 weight % oftitanium and all other trace metals, and carbon in an amount of lessthan about 0.75 weight %. The steel may comprise from about 25 to about50, or from about 30 to about 45 weight % nickel and or less than about1.4 weight % of silicon. The balance of the stainless steel issubstantially iron. In a further embodiment the stainless steel maycontain from 0 up to about 6 weight %, or from about 3 to about 6 weight% of aluminum.

In some embodiments, the present invention may also be used with nickeland/or cobalt based extreme austentic high temperature alloys (HTAs).The alloys may comprise a major amount of nickel or cobalt. The hightemperature nickel based alloys may comprise from about 50 to about 70,or from about 55 to about 65 weight % of Ni; from about 20 to about 10weight % of Cr; from about 20 to about 10 weight % of Co; and from about5 to about 9 weight % of Fe and the balance one or more of the traceelements noted below to bring the composition up to 100 weight %. Thehigh temperature cobalt based alloys may comprise from about 40 to about65 weight % of Co; from about 15 to about 20 weight % of Cr; from about20 to about 13 weight % of Ni; less than about 4 weight % of Fe and thebalance one or more trace elements as set out below and up to about 20weight % of W. The sum of the components adding up to 100 weight %.

In another embodiment, alloys may be used which contain up to about 12%Al, or less than about 7 weight %, or about 2.5 to about 3 weight %aluminum. In one embodiment, in the high cobalt and high nickel steelsthe aluminum may be present in an amount up to about 3 weight %, orbetween about 2.5 and about 3 weight %. In one embodiment, in the highchrome high nickel alloys (e.g. about 13 to about 50, or about 20 toabout 50, weight % of Cr and from about 20 to about 50 weight % of Ni)the aluminum content may range up to about 10, or less than about 7, orfrom about 2 to about 7 weight %.

In some embodiments of the invention the steel may further comprise anumber of trace elements including at least about 0.2 weight %, up toabout 3 weight %, or about 1.0 weight %, up to about 2.5 weight % or notmore than about 2 weight % of manganese; from about 0.3 to about 2, orabout 0.8 to about 1.6, or less than about 1.9 weight % of Si; less thanabout 3, or less than about 2 weight % of titanium, niobium (or lessthan about 2.0, or less than about 1.5 weight % of niobium) and allother trace metals; and carbon in an amount of less than about 2.0weight %. The trace elements are present in amounts so that thecomposition of the steel totals 100 weight %.

In one embodiment, the components of the serpentine reactor may betreated to create a spinel surface on the internal surface. There appearto be a number of treatments which may create a spinel surface. Onetreatment comprises (i) heating the stainless steel in a reducingatmosphere comprising from about 50 to about 100 weight % of hydrogenand from about 0 to about 50 weight % of one or more inert gases at rateof about 100° C. to about 150° C. per hour to a temperature from about800° C. to about 1100° C.; (ii) then subjecting the stainless steel toan oxidizing environment having an oxidizing potential equivalent to amixture of from about 30 to about 50 weight % of air and from about 70to about 50 weight % of one or more inert gases at a temperature fromabout 800° C. to about 1100° C. for a period of time from about 5 toabout 40 hours; and (iii) cooling the resulting stainless steel to roomtemperature at a rate of less than about 200° C. per hour.

In one embodiment, this treatment should be carried out until a there isan internal surface on one or more of the components of the serpentinereactor having a thickness greater than about 2 microns, or from about 2to about 25, or from about 2 to about 15 microns, or from about 2 toabout 10 microns and substantially comprising a spinel of the formulaMn_(x)Cr_(3-x)O₄ where x is a number from about 0.5 to about 2, or fromabout 0.8 to about 1.2. In one embodiment, X is 1 and the spinet has theformula MnCr₂O₄.

In some embodiments, the spinet surface covers not less than about 55%,or not less than about 60%, or not less than about 80%, or not less thanabout 95% of the stainless steel.

In a further embodiment there may be a chromia (Cr₂O₃) layerintermediate the surface spinel and the substrate stainless steel. Thechromia layer may have a thickness up to about 30 microns, or from about5 to about 24, or from about 7 to about 15 microns. As noted above thespinel overcoats the chromia geometrical surface area. In oneembodiment, there may be very small portions of the surface which mayonly be chromia and do not have the spinet overlayer. In this sense thelayered surface may be non-uniform. In one embodiment, the chromia layerunderlies or is adjacent not less than about 80, or not less than about95, or not less than about 99% of the spinel.

In a further embodiment the internal surface of one or more of thecomponents of the serpentine reactor may comprise from about 15 to about85 weight %, or from about 40 to about 60 weight % of compounds of theformula Mn_(x)Cr₃O₄ wherein x is from about 0.5 to about 2 and fromabout 85 to about 15 weight %, or from about 60 to about 40 weight % ofoxides of Mn and Si selected from MnO, MnSiO₃, Mn₂SiO₄ and mixturesthereof provided that the surface contains less than about 5 weight % ofCr₂O₃.

The present invention will further be described by reference to thefollowing demonstrations, which are merely illustrative of the inventionand are not intended to be limiting.

Demonstration:

One embodiment of the present invention will now be demonstrated withreference to FIGS. 3 and 4 and 5. FIG. 3 is the conventional “U” bend ofa serpentine reactor and FIGS. 4 and 5 are a “U” bend design modified inaccordance with the disclosure herein.

The finite element analysis software and computational fluid dynamicsoftware have been used to model NOVA Chemicals commercial ethylenecracking furnace piping at Joffre and Corunna. The models aresufficiently accurate to generally predict the commercial operation ofindustrial plants.

A numerical model of the conventional “U” bend as shown in FIG. 3, wascreated using a commercial finite element software program. Acomputational fluid dynamics program was also applied for the analysisof the conventional transfer line for gas at a temperature of greaterthan 600° C. and a flow rate of 3.97 Kg/s. The pressure drop and erosionrate were determined using ANSYS Fluent.

Using the shape deformation and optimization software Sculptor thecircular cross section of the conventional U bend or 180 degree bendcomponent computational or numerical model was deformed into anarbitrary shape independently at several transverse planes of theoriginal connecting pipe to generate a “deformed” shape based on aseries of deformation parameters per section. The ARQ of the resultingsections having a maximum ARQ substantially greater than 1.02. Themetallurgy of the pipe was maintained constant for these models. Thepressure drop, heat transfer and erosion rate were also calculated forthe “deformed” pipe.

The process was applied iteratively until no further improvements inpressure drop or erosion rate were found. The resulting geometry and ARQvalues are shown in FIG. 4 and FIG. 5. Table 1 demonstrates in this casethat the heat transfer declined. This demonstrates that in amulti-objective optimization not all performance parameters willnecessarily improve. However, given the short resident time of thereactants in a U bend the reduction in heat transfer (which may resultfrom better flow rates) is acceptable given the reduction in pressuredrop and erosion rate. Another optimization could be run to improve heattransfer, it could be deemed acceptable or it could be improvedindependent of the various embodiments of the present invention (forexample, finned tubes).

Table 1 is a summary of representative data from the computer modeling.

TABLE 1 Reduction in Total Heat Simulation or Iteration PressureReduction in Transfer Rate Number Drop Erosion Rate Improvement 1  0% 0%  0% (Base design in FIG. 3) 2 39% 24% −5% 3 41% 23% −5% 4 47% 26%−6% 5 49% 32% −6% 6 49% 30% −6%

Although the change in ARQ appears to be moderate, the resulting changein reactor performance has been dramatic.

The present invention has been described with reference to certaindetails of particular embodiments thereof. It is not intended that suchdetails be regarded as limitations upon the scope of the inventionexcept insofar as and to the extent that they are included in theaccompanying claims.

1. A method to crack a gaseous hydrocarbon comprising passing thehydrocarbon through a reactor having a reduced calculated pressure dropacross a flow path having a continuously smooth and differentiableperimeter and centerline of one or more first straight pipe sections ofa serpentine reactor by not less than 10% relative to a second pipesection having a flow path having an ARQ from 1.0 to 1.02 where ARQ isdefined as the ratio of aspect ratio (AR) to isoperimetric quotient (Q)of a section or segment of the flow passage perpendicular to thedirection of flow (AR/Q) and further where AR=Long/short and$Q = \frac{4\pi \; A}{L^{2}}$ where A is area of a cross section ofthe flow path and L is the perimeter of the flow path comprising varyingthe flow passage over 90% of its length from 5% from the inlet andoutlet so that the ARQ is from about 1.02 to about 1.15 at a temperaturefrom 850° C. to 1000° C.
 2. The method according to claim 1, wherein thefirst pipe sections are part of a high pressure olefin polymerizationreactor wherein the hydrocarbon comprises ethane.
 3. The methodaccording to claim 1, wherein the first pipe section is part of thefurnace tubes of an olefin cracker.
 4. The method according to claim 3,wherein over 90% of the flow passage does not change by more than 7%over an about 5% length of the flow path.
 5. The method according toclaim 4, wherein the ARQ at one or more sections over said 90% of thelength of the flow passage is from about 1.02 and about 1.12.
 6. Themethod according to claim 5, wherein the ARQ over said 80% of the lengthof the flow passage does not change by more than about 5% over an about5% length of the flow path. 7-22. (canceled)
 23. The method according toclaim 6, wherein the ARQ at one or more sections over said remainingabout 80% of the length of the flow passage is from about 1.02 and about1.15.
 24. The method according to claim 23, wherein the serpentinereactor has an increasing cross sectional area in the direction of flowsuch that the angle between the transverse normal vector and the pipewalls range from about 0° to about 85°.
 25. The method according toclaim 24 wherein the flow passage has a smooth curve in its longitudinaldirection which although may change rapidly, does not include abrupt,sharp changes of internal section (steps) and a radius of curvature onthe internal surface of the curve from unbound (straight) to half thevertical of the section radius.
 26. The method according to claim 25,wherein the first pipe section comprises from about 20 to about 50weight % of chromium, about 25 to about 50 weight % of Ni, from about1.0 to about 2.5 weight % of Mn less than about 1.0 weight % of niobium,less than about 1.5 weight % of silicon, less than about 3 weight % oftitanium and all other trace metals and carbon in an amount less thanabout 0.75 weight % and from about 0 to about 6 weight % of aluminum.27. The method according to claim 25, wherein said first pipe sectioncomprises from about 40 to about 65 weight % of Co; from about 15 toabout 20 weight % of Cr; from about 20 to about 13 weight % of Ni; lessthan about 4 weight % of Fe and the balance of one or more traceelements and up to about 20 weight % of W the sum of the componentsadding up to 100 weight %.
 28. The method according to claim 25, whereinsaid first pipe section comprises from about 55 to about 65 weight % ofNi; from about 20 to about 10 weight % of Cr; from about 20 to about 10weight % of Co; and from about 5 to about 9 weight % of Fe and thebalance one or more of the trace elements.
 29. The method according toclaim 2, wherein over said 90% of the flow passage does not change bymore than about 7% over an about 5% length of the flow path.
 30. Themethod according to claim 29, wherein the ARQ at one or more sectionsover said 90% of the length of the flow passage is from about 1.02 andabout 1.12.
 31. The method according to claim 30, wherein the ARQ oversaid about 80% of the length of the flow passage does not change by morethan about 5% over an about 5% length of the flow path.
 32. The methodaccording to claim 31, wherein the ARQ at one or more sections over saidremaining about 80% of the length of the flow passage is from about 1.02and about 1.15.
 33. The method according to claim 32, wherein theserpentine reactor has an increasing cross sectional area in thedirection of flow such that the angle between the transverse normalvector and the pipe walls range from about 0° to about 85°.
 34. Themethod according to claim 33 wherein the flow passage has a smooth curvein its longitudinal direction which although may change rapidly, doesnot include abrupt, sharp changes of internal section (steps) and aradius of curvature on the internal surface of the curve from unbound(straight) to half the vertical of the section radius.
 35. The methodaccording to claim 34, wherein said first pipe section comprises fromabout 20 to about 50 weight % of chromium, about 25 to about 50 weight %of Ni, from about 1.0 to about 2.5 weight % of Mn less than about 1.0weight % of niobium, less than about 1.5 weight % of silicon, less thanabout 3 weight % of titanium and all other trace metals and carbon in anamount less than about 0.75 weight % and from about 0 to about 6 weight% of aluminum.
 36. The method according to claim 34, wherein said firstpipe section comprises from about 40 to about 65 weight % of Co; fromabout 15 to about 20 weight % of Cr; from about 20 to about 13 weight %of Ni; less than about 4 weight % of Fe and the balance of one or moretrace elements and up to about 20 weight % of W the sum of thecomponents adding up to 100 weight %.
 37. The method according to claim34, wherein said first pipe section comprises from about 55 to about 65weight % of Ni; from about 20 to about 10 weight % of Cr; from about 20to about 10 weight % of Co; and from about 5 to about 9 weight % of Feand the balance one or more of the trace elements.
 38. A method toreduce the normalized calculated erosion rate across the flow pathhaving a continuously smooth and differentiable perimeter and centerlineof one or more first straight pipe sections of a serpentine reactor bynot less than 10% relative to a second pipe section having a flow pathhaving an ARQ from 1.0 to 1.02 where ARQ is defined as the ratio ofaspect ratio (AR) to isoperimetric quotient (Q) of a section or segmentof the flow passage perpendicular to the direction of flow (AR/Q) andfurther where AR-Long/Short and $Q = \frac{4\pi \; A}{L^{2}}$ where Ais area of a cross section of the flow path and L is the perimeter ofthe flow path comprising varying the flow passage over 90% of its lengthfrom 5% from the inlet and outlet so that the ARQ is from about 1.02 toabout 1.15.